Pith Number

pith:LIEPDDRD

pith:2006:LIEPDDRDUFG47GRAVXYYY4IER4

not attested not anchored not stored refs pending

The Tits alternative for generalized triangle groups of type (3,4,2)

Gerald Williams, James Howie

arxiv:math/0603682 v1 · 2006-03-29 · math.GR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LIEPDDRDUFG47GRAVXYYY4IER4}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T04:33:27.512568Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a08f18e23a14dcf9a20adf18c71048f2f648d8db6d672c4db008db641ef6452

Aliases

arxiv: math/0603682 · arxiv_version: math/0603682v1 · doi: 10.48550/arxiv.math/0603682 · pith_short_12: LIEPDDRDUFG4 · pith_short_16: LIEPDDRDUFG47GRA · pith_short_8: LIEPDDRD

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/LIEPDDRDUFG47GRAVXYYY4IER4 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5a08f18e23a14dcf9a20adf18c71048f2f648d8db6d672c4db008db641ef6452

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a3b6f386723d262de70215f4af36d0fa5929e5e7e041cde93c73b8c9f7f262b",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GR",
    "submitted_at": "2006-03-29T12:47:32Z",
    "title_canon_sha256": "948510449eb2781ea3060f696cd83d895496e35cd494a2db53132b8e557942be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0603682",
    "kind": "arxiv",
    "version": 1
  }
}